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A127059
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Column 2 of triangle A127058.
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3
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3, 12, 108, 1332, 19908, 342252, 6583788, 139380372, 3211960068, 79950396492, 2137119431148, 61065403377012, 1858069709657028, 60006976422450732, 2050924514408985708, 73988085260209757652, 2810535115787602525188
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OFFSET
| 0,1
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COMMENTS
| Column 0 of triangle A127059 is A000698, the number of shellings of an n-cube, divided by 2^n n!. Column 1 of triangle A127059 is A115974, the number of Feynman diagrams of the proper self-energy at perturbative order n.
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FORMULA
| a(0)=3 and for n>0 a(n)=(1/2)*(c(n+3)-3*c(n+2)-sum(a(k)*(c(n+2-k)-c(n+1-k)),k=0..n-1) with c(n)=(2*n)!/(2^n*n!) [From Groux roland (roland.groux(AT)orange.fr), Nov 14 2009]
G.f.: A(x) = (1 - T(0))/x, T(k) = 1 - x*(k+3)/T(k+1) (continued fraction). - Sergei N. Gladkovskii, Dec 13 2011
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CROSSREFS
| Cf. A127058; other columns: A000698, A115974; A127060.
Sequence in context: A141535 A111485 A080447 * A178013 A068099 A032113
Adjacent sequences: A127056 A127057 A127058 * A127060 A127061 A127062
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KEYWORD
| nonn
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AUTHOR
| Paul D. Hanna (pauldhanna(AT)juno.com), Jan 04 2007
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